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This lesson provided by:
Author:Tim McKenzie
System: Shelby County
School: Helena Middle
Lesson Plan ID: 33035

Painter Problems


This lesson will allow students to become familiar with ratios. In this investigative lesson students will compare ratios and determine equivalent ratios. This is an introductory lesson to be used as part of a unit. 

This is a College- and Career-Ready Standards showcase lesson plan.

Content Standard(s):
MA2015(6) 1. Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6-RP1]
MA2015(6) 3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6-RP3]
Local/National Standards:

Math Practice Standards: 

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others. 

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning. 

Primary Learning Objective(s):

I CAN identify and develop ratios in real world situations.

I CAN identify equivalent ratios.


Additional Learning Objective(s):  
Approximate Duration of the Lesson: 61 to 90 Minutes
Materials and Equipment:

Discussion Cards (provided in the attachment section)

Ratio Exit Slip (provided in the attachment section)

Painter Problems Activity Guide

Investigative Activity Rubric

Chart paper

Math Toolbox which include the following: pencil, paper, graph paper, markers, scissors, glue, calculator, and sticky notes

Technology Resources Needed:

Interactive Whiteboard (Optional) with required software

Document camera or projector

Access to search engine (individually or whole group)


The teacher must prepare the appropriate number of math tool boxes for the class; several students can use one tool box. 

The teacher must make the appropriate number of copies of the Painter Problems Activity guide; to promote student collaboration several students may use one guide.

The teacher must prepare Ratio Discussion Cards (found in attachments) or ratio models may be created on the interactive whiteboard software or the application of paint.

The teacher must make the appropriate number of Ratio Exit Slips (found in attachments); each student will need one Exit Slip.

The students must have prior knowledge of fractions and how to develop equivalent fractions. 



1. The teacher will conduct a math discussion on ratios, using the Discussion Cards (found in attachments). The teacher will display Ratio card 1. The teacher will ask students to give the fraction of the red tiles, and ask the students "What does a fraction tell us?" The students will give feedback on the significance of the numerator and denominator. The teacher will then introduce “ratio” as a math word. The teacher will identify a ratio as a number that compares two quantities and provide the three ways to write a ratio (a to b; a/b; a:b). The teacher will ask, “What is the ratio of red tiles to white tiles?” “White to red?” “Red to the total amount?” The teacher will continue this discussion with the remaining cards. The teacher will ask the students the main difference between a fraction and a ratio.

2. Once the discussion subsides, the teacher will allow students time to search "Ratios in Advertisements." Students will discuss the different ratios they view on the Web (an example: 2 out of 3 people choose us). If every student cannot individually search, students may work in groups or teacher can lead a whole group search.

3. The teacher will transition students into the investigative activity, Painter Problems. To build background knowledge the teacher will explain how paint is mixed at the local hardware store. "Using a white base, workers must provide the appropriate drops of dye to get the desired color. Today there are computers for this, but many times computers fail." To introduce the activity the teacher will tell the students that they have a summer job at a paint store where the computer does not work. Using the ratios provided, they must fulfill the orders for the customers. 

4. The students will begin the investigation. Students may work individually or collaboratively. 

5. Once adequate time (30-45 minutes) is given, the students will share their finding on the document camera. (If a document camera is not available, students may present their work in the front of the class, this is where the students would need chart paper). As the students are sharing, the teacher is acting as the facilitator and coach asking questions that drive ratio understanding. "How do you know that ratio is equivalent to the first ratio?" "How did you know to do _______?" "Did someone do this differently or find a different answer?" 

6. Toward the end of class, the teacher will distribute the Exit Slip (found in attachments). 

Attachments:**Some files will display in a new window. Others will prompt you to download. PainterProblems.pdf
Assessment Strategies:

Formal Formative Assessment: Ratio Exit Slip (found in attachments)

Formal Assessment: Using the Investigative Activity Rubric (found in attachments) teacher will evaluate students' work.

Informal Formative Assessment: As the students are working, the teacher will act as the facilitator and coach. Teacher will ask questions to evaluate students (i.e. How do you know ______? What did you do to get that?) Teacher may pull small groups during investigation on a needs basis.



The investigation has an included extension on the Painter Problem Activity Sheet (found in attachments).


Because this is part of a unit, teacher may develop small groups based on the Ratio Exit Slip or informal questioning as part of the investigative activity.

Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material Environment
Time Demands Materials
Attention Using Groups and Peers
Assisting the Reluctant Starter Dealing with Inappropriate Behavior

Be sure to check the student's IEP for specific accommodations.
Variations Submitted by ALEX Users:
Alabama Virtual Library
Alabama Virtual Library

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The University of Alabama at Birmingham
The University of Alabama at Birmingham
The Malone Family Foundation
The Malone Family Foundation
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